Depends which country you are in. In most English-speaking countries we were taught "half-up" and think it means "half-away-from-zero", which you can find under RoundingMode as HALF_UP.
There is no absolute or right way to round halves: should you round up, down, towards 0, away from 0, towards an odd number, towards an even number, or even randomly? You will find a bit about IEEE-754R
here, but I haven't read enough to know the rationale behind their choosing a particular rounding mode (they actually recommend half-towards-even). I believe the rationale of rounding one way half the time and the other way the rest is the correct explanation, but I don't know whether it is a better explanation than any of the other rounding modes. If there is no absolutely right way to round numbers, then we cannot consider the other ways as absolutely wrong.
And it definitely wasn't stone age when I was at school with paper and pencil (and I am probably older than you
). We thought we were modern.